Main Article Content
Let be a -uniform, -regular, connected hypergraph of order and size for some . For , let , the transversal number of a hypergraph in which for all are investigated. In this paper, we interested in studying some properties of an edge-intersection graph of a hypergraph such as the vertex cover, the matching, and the independent set. We prove that is a bipartite graph and the transversal number of is equal to the vertex covering number of .
Alain, B. (2013). Hypergraph Theory An Introduction. Switzerland: Springer International Publishing.
Baranyai, Zs. (1975). On the factorization of the complete uniform hypergraph. In Hajnal, A. Rado, R. & Sós, V. T. (eds.), Infinite and Finite Sets. Colloquium held at Keszthely, June 25-July 1, 1973. Dedicated to Paul Erdös on his 60th Birthday (pp. 91-108). Amsterdam, Netherlands: North-Holland.
Bouchou, A. & Blidia, M. (2014). On the k-independence number in graphs. Australasian Journal of Combinatorics 59 (2), 311–322.
Bujtas, Cs., Henning, M. A. & Tuza, Zs. (2012). Transversals and domination in uniform hypergraphs. European Journal of Combinatorics 33, 62-71. https://doi.org/10.1016/-j.ejc.2011.08.002
Chvatal, V. & McDiarmid, C. (1992). Small transversals in hypergraphs. Combinatorica 12, 19-26. https://doi.org/10.1007/BF01191201
Cockayne, E. J., Hedetniemi, S. T. & Slater, P. J. (1979). Matchings and transversals in hypergraphs, domination and independence-in trees. Journal of Combinatorial Theory, Series B 27, 78-80. https://doi.org/10.1016/0095-8956(79)90044-3
Diestel, R. (2000). Graph Theory. New York: Springer-Verlag.
Harant, J. & Rautenbach, D. (2011). Independence in connected graphs. Discrete Applied Math 159 (1), 79-86. https://doi.org/10.1016/j.dam.2010.08.029
Henning, M. A., Lowenstein, C. & Rautenbach, D. (2012). Independent sets and matchings in subcubic graphs. Discrete Mathematics 312 (11), 1900-1910. https://doi.org/10.101-6/j.disc.2012.03.002
Henning, M. A. & Yeo, A. (2008). Hypergraphs with large transversal number and with edge sizes at least three. Journal of Graph Theory 59, 326-348. https://doi.org/10.1-002/jgt.20340
Zhang, Z. & Lou, D. (2009). Notes on bipartite graphs with a perfect matching and digraph. Advances and Applications in Discrete Mathematics 3 (2), 155-164.